Quantum correlations (entanglement) [1]} form a key concept towards the foundational understanding of quantum mechanics, and has been realized as a precious resource for various tasks that are impossible in classical domian like quantum teleportation, cryptograpgy, and various other processings[2]}, [3]}, [4]}, [5]}.The deeper insights into the dynamics of quantum correlations is of great importance, since the real quantum system always interacts with its bath that leads to decoherence of quantum superpositions and entanglement degradation [6]}, [7]}, [8]}, [9]}, [10]}. This system-bath dynamics is categorized either as Markovian or non-Markovian [11]}, [12]}, [13]}. In a Markov process, the system loses information to environment irreversibly. However, many quantum systems posses a pronounced
non-Markovian behavior in which there is flow of information back to system, signifying the presence of quantum memory effects [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}. The physical realization and
control of dynamical processes in open quantum systems plays a decisive role, for example, in recent proposals for the generation of entangled states [23]}, [24]}, for schemes of dissipative quantum computation [25]}, [26]}, for the design of quantum memories [27]} and for the enhancement of the efficiency in quantum metrology [28]}. Moreover, in the regime where non-Markovian effects are important, the presence of system-bath correlations invalidates the initial state in which the system and the bath are independent. Especially in the experimentally relevant case where the qubit system is excited out of equilibrium and the subsequent dynamics is probed, a proper treatment of the initial state is crucial.
